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Communications in Theoretical Physics

Does the Hawking effect have the same impact on quantum entanglement and coherence in curved spacetime?

Yu-Xuan Wang, Shu-Min Wu, Zhihong Liu

Published Jun 17, 2026• 0 citations
Publisher

Abstract

Abstract We investigate how the Hawking effect reshapes distinct quantum resources of Dirac fields in Schwarzschild spacetime beyond the single-mode approximation. By quantifying quantum entanglement and coherence using the negativity, the l 1 -norm of coherence and the relative entropy of coherence, we observe a significant asymmetry in their response to gravitational effects. While the Hawking effect monotonically degrades entanglement and drives it toward a finite residual value, quantum coherence is instead monotonically amplified with increasing Hawking temperature, revealing the black hole as an effective decohering environment for nonlocal correlations but a coherence-enhancing mechanism for local superposition. Notably, we further find that under the influence of the Hawking effect, the maximally entangled state does not necessarily correspond to the largest initial negativity. In fact, its value may even be smaller than that of certain non-maximally entangled states. Our results demonstrate that gravity acts in a highly nonuniform manner on different facets of quantumness and highlight the necessity of resource-adapted state engineering for relativistic quantum information processing near the event horizon of the black hole.

DOI
10.1088/1572-9494/ae7e69

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Abstract We investigate how the Hawking effect reshapes distinct quantum resources of Dirac fields in Schwarzschild spacetime beyond the single-mode approximation. By quantifying quantum entanglement and coherence using the negativity, the l 1 -norm of coherence and the relative entropy of coherence, we observe a significant asymmetry in their response to gravitational effects. While the Hawking effect monotonically degrades entanglement and drives it toward a finite residual value, quantum coherence is instead monotonically amplified with increasing Hawking temperature, revealing the black hole as an effective decohering environment for nonlocal correlations but a coherence-enhancing mechanism for local superposition. Notably, we further find that under the influence of the Hawking effect, the maximally entangled state does not necessarily correspond to the largest initial negativity. In fact, its value may even be smaller than that of certain non-maximally entangled states. Our results demonstrate that gravity acts in a highly nonuniform manner on different facets of quantumness and highlight the necessity of resource-adapted state engineering for relativistic quantum information processing near the event horizon of the black hole.
We investigate the influence of the Garfinkle-Horowitz-Strominger (GHS) dilaton black hole on different quantum resources of Dirac fields beyond the single-mode approximation. By employing the negativity to characterize quantum entanglement and the l1l_1l1​-norm and the relative entropy of coherence to characterize quantum coherence, we demonstrate that these resources exhibit remarkably different responses to the gravitational field. Specifically, increasing the dilaton parameter continuously suppresses quantum entanglement, leaving only a finite residual amount in the strong-gravity regime, whereas quantum coherence is enhanced, indicating that the dilaton-induced spacetime affects nonlocal quantum correlations and local quantum superposition in fundamentally different ways. Furthermore, we show that an initially maximally entangled state does not always possess the largest negativity after propagating in the GHS dilaton spacetime; instead, under appropriate conditions, certain non-maximally entangled states can retain stronger entanglement than the maximally entangled one. These findings reveal the resource-dependent nature of gravitational effects in dilaton black hole backgrounds and provide new insights into the manipulation and protection of quantum resources for relativistic quantum information processing in curved spacetime.
Abstract In this work, we explore the impact of the Hawking effect on quantum nonlocality, specifically the maximum violation of the Bell-CHSH inequality, for both scalar and Dirac fields within Schwarzschild spacetime. We reveal the nuanced behavior of the Bell-CHSH inequality as the Hawking temperature (HT) varies. For scalar fields, we observe distinct degradation patterns in the Bell-CHSH inequality, influenced by the state parameter α and its normalized counterpart 1 − α 2 . In contrast, Dirac fields exhibit two distinct degradation trajectories, each converging to different nonzero minimum values as HT approaches infinity T → ∞ , however, this does not apply to the maximally entangled state. Remarkably, the maximum violation of Bell-CHSH inequality becomes zero for scalar fields at infinite HT, while it stabilizes at a finite nonzero value for Dirac fields. Additionally, the quantum nonlocality robustness of the Dirac fields is stronger than that of the scalar fields. Therefore, this study enhances our understanding of the dynamic characteristics of nonlocality within scalar and Dirac fields near a Schwarzschild black hole.
We investigate the quantum entanglement properties of the Dirac field near a charged Reissner--Nordström black hole, incorporating the effects of Hawking radiation within the framework of quantum field theory in curved spacetime. Using concurrence C C C and Bures distance B B B as measures of entanglement, we analyze how quantum correlations evolve with respect to the electric charge Q Q Q of the black hole, the frequency ω ωω of fermionic modes, and the initial entanglement angle θ θθ. Our results show that the electric charge Q Q Q enhances decoherence inside the event horizon while, counterintuitively, temporarily increasing accessible entanglement outside. The Hawking effect induces an apparent loss of entanglement for an external observer, due to correlation transfer to inaccessible regions. High-frequency modes ω ωω exhibit greater resilience to gravitational effects, maintaining robust correlations near the horizon. These findings highlight the redistribution of entanglement in a multipartite system in curved spacetime, with significant implications for quantum information in relativistic and gravitational contexts.
Abstract The black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.
Abstract Most previous studies on relativistic quantum information have primarily focused on the vacuum state ∣0⟩|0\rangle ∣0⟩ | 0 ⟩ and the first excited state ∣1⟩|1\rangle ∣1⟩ | 1 ⟩ in two-mode entangled systems. In this work, we go beyond these limitations by considering arbitrary q -th excited states ∣q⟩|q\rangle ∣q⟩ | q ⟩ , aiming to investigate their role in preserving quantum resources. We analyze the influence of the Hawking effect on multipartite quantum states in the Schwarzschild spacetime, with particular attention to quantum entanglement and coherence. Our results show that, under the influence of the Hawking effect, increasing the excitation number q leads to a reduction in quantum entanglement and mutual information, while enhancing quantum coherence. This indicates that the Hawking effect on excited multipartite states tends to degrade quantum correlations but simultaneously protects quantum coherence in curved spacetime. Therefore, when implementing quantum information protocols in gravitational settings, reducing the excitation number q is favorable for maintaining entanglement, whereas increasing q may be advantageous for tasks that rely on quantum coherence in relativistic quantum information processing.
Abstract In the past two decades, the exploration of quantumness within Schwarzschild spacetime has garnered significant interest, particularly regarding the Hawking radiation’s impact on quantum correlations and quantum coherence. Building on this foundation, we investigate how Hawking radiation influences maximal steered coherence (MSC)-a crucial measure for gauging the ability to generate coherence through steering. We find that as the Hawking temperature increases, the physically accessible MSC degrade while the unaccessible MSC increase. This observation is attributed to a redistribution of the initial quantum correlations, previously acknowledged by inertial observers, across all bipartite modes. In particular, we find that in limit case that the Hawking temperature tends to infinity, the accessible MSC equals to 1/21/\sqrt{2}1/2​ 1 / 2 of its initial value, and the unaccessible MSC between mode A and B‾\overline{B}B B ¯ also equals to the same value. Our findings illuminate the intricate dynamics of quantum information in the vicinity of black holes, suggesting that Hawking radiation plays a pivotal role in reshaping the landscape of quantum coherence and entanglement in curved spacetime. This study not only advances our theoretical understanding of black hole thermodynamics but also opens new avenues for investigating the interface between quantum mechanics and general relativity.